What is the meaning of laying claim?

noun

• The act of taking possession of or power over something.
  • usage: "his assumption of office coincided with the trouble in Cuba"; "the Nazi assumption of power in 1934"; "he acquired all the company's assets for ten million dollars and the assumption of the company's debts"
  • synonyms: assumption

verb

• Demand as being one's due or property; assert one's right or title to.
  • usage: "He claimed his suitcases at the airline counter"; "Mr. Smith claims special tax exemptions because he is a foreign resident"
  • synonyms: claim, lay claim, arrogate